Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-3x+2y &= 2 \\ -6x-2y &= -5\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-9x = -3$ Divide both sides by $-9$ and reduce as necessary. $x = \dfrac{1}{3}$ Substitute $\dfrac{1}{3}$ for $x$ in the top equation. $-3( \dfrac{1}{3})+2y = 2$ $-1+2y = 2$ $2y = 3$ $y = \dfrac{3}{2}$ The solution is $\enspace x = \dfrac{1}{3}, \enspace y = \dfrac{3}{2}$.